Ask once, at resolution
A single question with a one-click answer, attached to the resolution notification. Anything longer is a survey, and surveys are answered mostly by the furious and the delighted.
Expect a low response rate and do not chase it
Ten to twenty per cent is normal and sufficient. Chasing responses annoys the customers you are trying to please and biases the result.
The follow-up matters more than the score
Every negative rating should open a ticket to a team lead automatically. A bad score nobody acts on is worse than not asking, because the customer now knows you asked and did nothing.
Report it alongside speed
Satisfaction read next to first response time and reopen rate tells a coherent story. Read alone it is a mood ring.